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Abstract

In general, diffusion model-based MRI reconstruction methods incrementally remove artificially added noise while imposing data consistency to reconstruct the underlying images. However, real-world MRI acquisitions already contain inherent noise due to thermal fluctuations. This phenomenon is particularly notable when using ultra-fast, high-resolution imaging sequences for advanced research, or using low-field systems favored by low- and middle-income countries. These common scenarios can lead to sub-optimal performance or complete failure of existing diffusion model-based reconstruction techniques. Specifically, as the artificially added noise is gradually removed, the inherent MRI noise becomes increasingly pronounced, making the actual noise level inconsistent with the predefined denoising schedule and consequently inaccurate image reconstruction. To tackle this problem, we propose a posterior sampling strategy with a novel NoIse Level Adaptive Data Consistency (Nila-DC) operation. Extensive experiments are conducted on two public datasets and an in-house clinical dataset with field strength ranging from 0.3T to 3T, showing that our method surpasses the state-of-the-art MRI reconstruction methods, and is highly robust against various noise levels. The code for Nila is available at \url{https://github.com/Solor-pikachu/Nila}.

Links to Paper and Supplementary Materials

Main Paper (Open Access Version): https://papers.miccai.org/miccai-2024/paper/1511_paper.pdf

SharedIt Link: https://rdcu.be/dV5Ep

SpringerLink (DOI): https://doi.org/10.1007/978-3-031-72104-5_48

Supplementary Material: https://papers.miccai.org/miccai-2024/supp/1511_supp.pdf

Link to the Code Repository

https://github.com/Solor-pikachu/Nila

Link to the Dataset(s)

N/A

BibTex

@InProceedings{Hua_Noise_MICCAI2024,
        author = { Huang, Shoujin and Luo, Guanxiong and Wang, Xi and Chen, Ziran and Wang, Yuwan and Yang, Huaishui and Heng, Pheng-Ann and Zhang, Lingyan and Lyu, Mengye},
        title = { { Noise Level Adaptive Diffusion Model for Robust Reconstruction of Accelerated MRI } },
        booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2024},
        year = {2024},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 15007},
        month = {October},
        page = {498 -- 508}
}

Reviews

Review #1

  • Please describe the contribution of the paper

    The manuscript proposes a diffusion-based under-sampled MRI reconstruction method that takes the inherent measurement noise into account during reverse diffusion (e.g., via posterior sampling). Results are presented on the original fastMRI dataset, on noisier versions of it obtained synthetically, as well as on a prospectively under-sampled dataset without ground-truth.

  • Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

    The topic is timely and the paper is well-written. The quantitative experimental results are good.

  • Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

    Equation (7) appears to be technically incorrect, which propagates errors to equation (9) and the entire methodology. Details involved in the experimental evaluation are lacking (how was noise added to the data?)

  • Please rate the clarity and organization of this paper

    Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The authors claimed to release the source code and/or dataset upon acceptance of the submission.

  • Do you have any additional comments regarding the paper’s reproducibility?

    How noisy data was produced is not sufficiently clear, given that it is a central aspect of the experiments.

  • Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html

    • There is a well-known issue with approximating the gradient of the data consistency term that is not properly addressed by the manuscript. This makes equation (7) incorrect given that it is stated as an equality, and not an approximation.

    • The approximation of log p(y x_t) should be taken into account. This term is not tractable in general, and there are several ways of approximating it:
    • As reference [11] cited in the manuscript does.
    • By using the DPS method in Chung, Hyungjin, et al. “Diffusion posterior sampling for general noisy inverse problems.” arXiv preprint arXiv:2209.14687 (2022), Page 5, Equation (15).
    • By adding noise to the measurements y themselves to form y_t in the reverse diffusion process as in Song, Yang, et al. “Solving inverse problems in medical imaging with score-based generative models.” arXiv preprint arXiv:2111.08005 (2021), Page 4, Section 3.

    • It would also be possible to learn a conditional diffusion model for this term as mentioned in Song, Yang, et al. “Solving inverse problems in medical imaging with score-based generative models.” arXiv preprint arXiv:2111.08005 (2021).

    • Commenting on which approximation was used, why was it chosen, and how it affects the proposed formalism would be necessary to improve the manuscript.

    • The technical error in (7) propagates to (9), gives that approximating the gradient in (7) will perturb the entire reverse diffusion chain. This perturbation should be acknowledged and discussed with care.

    • It is unclear why a linear attenuation function was not used across all reverse steps, instead of the step-attenuation function proposed. This makes the hyper-parameter \gamma hard to justify and select in practice, and it is also not explained how this two-regime reverse diffusion ties in with the formalism in (9).

    • It is unclear what the authors meant by “we set \sigma_y = 0.05” - the whole idea is that this noise is already present in the scans, so it would have been better advised that the authors just estimate this value via a quick calibration scan, as acknowledged in Section 2.

    • It is unclear how the additional noise was added: for example, when the authors present the values in Table 6 of \sigma, is this the standard deviation of the added noise, or of the added noise plus the noise inherent to the measurements (which should have been properly estimated as per the point above)?
  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making

    Reject — should be rejected, independent of rebuttal (2)

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    While the topic is timely and the experiments are detailed, there are several major issues regarding technical correctness and methodology that affect the manuscript in its current form.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed

    Weak Accept — could be accepted, dependent on rebuttal (4)

  • [Post rebuttal] Please justify your decision

    The authors have agreed to properly cite a justification for their assumption made in Eq.7.



Review #2

  • Please describe the contribution of the paper

    This paper proposes a method to take into account the level of noise in the observations when training a diffusion model for accelerated MRI. The authors estimate the level of noise from a zero-filled image, and then use it to attenuate the impact of data consistency when the noise level of the generated image reaches the noise level in the training data. They validate their methods on fastMRI, low-field data, clinical data as well as prospectively acquired data.

  • Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
    1. Intuitive approach to an often neglected problem: how to keep improving the reconstruction of undersampled data when data consistency would be adding the noise present in the ground truth.
    2. Extended and convincing validation of the method : fastMRI, low-field data (a setting known as yielding lower SNR), clinical data and prospectively accelerated DWI data. I really commend the authors for doing the effort of including prospectively acquired data.
    3. Comparison to relevant SotA approaches: both classical, and DL-based methods.
    4. Ablation study on the impact of the added hyper-parameter on the reconstruction.
  • Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
    1. Major. The method introduces additional hyper-parameters: the estimated noise level $\sigma_y$, $\gamma$, $k$, $b$. While the authors showed the influence of $\sigma_y$ on reconstruction, it is not clear to me how the other parameters are set/tuned. The authors mention that $\sigma_y$ is easy to tune with the noise level of a zero-filled reconstruction. Could they use it systematically and so effectively “remove” one hyper-parameter?
    2. The authors do not justify what they choose their linear attenuation function. Other shapes, that do not induce a discontinuity, would seem more natural to me. I would be afraid that such discontinuity could induce some instability during training. In addition, if the aim of the authors is to keep the denoising schedule $\beta_t$ unchanged, why do the authors not use a an attenuation function from the beginning?
    3. Minor (ablation). For the sake of clarity, it would be great to add to the results Table a line for the authors’ diffusion model without the Nila DC, to clearly separate the contribution of the i) backbone ii) the Nila DC without added noise and iii) the Nila DC when noise has been added.
    4. Minor (Clarity). In the methods part, the noise variable is described inconsistently: sometimes as the random variable $\eta$, sometimes as $\sigma_y$, which does not help the reader clearly understand whether the text speaks of a scalar or a vector. In particular, I think that you should have $\eta$ in equations (8) and (10).
    5. Minor. The authors did not acknowledge the work of the group of Jong Chul Ye who have multiple important contributions regarding diffusion models for accelerated MRI (e.g. [1,2]) that are in my opinion directly relevant to this paper.

    [1] Chung, H. & Ye, J. C. (2022). Score-based diffusion models for accelerated MRI. MedIA. [2] Chung, H et al. (2023). Diffusion posterior sampling for general noisy inverse problems. ICLR.

  • Please rate the clarity and organization of this paper

    Very Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The authors claimed to release the source code and/or dataset upon acceptance of the submission.

  • Do you have any additional comments regarding the paper’s reproducibility?

    In its current state, the description in the paper isn’t sufficient for reproducibility, but accessing the code will surely fix this.

  • Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html

    This is a very nice paper, and the validation carried out is very thorough. Besides the limitations mentioned above, I have a few suggestions and questions.

    • For consistency of notation, the user should use bold fonts for greek letters that describe vectors (e.g. eq. 8 and 10).
    • The authors mention that even without adding extra noise, their algorithm outperforms other methods. This isn’t totally clear to me why this is the case. It it because the reconstruction can go past the noise in the ground truth data to improve the reconstruction?
    • Following up on the previous question, there is inherent noise even in ground truth data, and Nila could potentially help get an image that is “better” than the ground truth. In this case, could there be other measures than PSNR or SSIM that would better reflect the quality of the reconstructed image? I could imagine cases where the model would get a worse score for having an image that is less noisy than the ground truth. How can you account for this?
  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making

    Weak Accept — could be accepted, dependent on rebuttal (4)

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    While the paper has some limitations, the approach is interesting and the paper presents extensive validation of the method, even including prospectively acquired data. The strong validation justifies a presentation of the paper at the conference, but I would like to read the authors’ rebuttal prior to potentially increasing my score.

  • Reviewer confidence

    Confident but not absolutely certain (3)

  • [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed

    Accept — should be accepted, independent of rebuttal (5)

  • [Post rebuttal] Please justify your decision

    After reading the rebuttal, I believe that the paper should be accepted. The method is novel, interesting and well evaluated. The rebuttal clarifies some typos and important definitions of parameters.

    I am not an expert on diffusion models, but I have trouble understanding the concern of R1 (so please forgive me if my next statement misses the point). However, like the authors explain in their rebuttal, I think that ∇xt log p(y x_t) can be written in a closed form in the case of MRI, as it is described by the simple forward model given in equation 1. I don’t understand why it would need to be approximated in this case. If this is the case then, I think that the biggest objection of R1 to the acceptance of the paper would be answered. However, I agree with R1 that discussing whether an approximation of the likelihood is needed would be beneficial to the paper.



Review #3

  • Please describe the contribution of the paper

    In this paper, reconstruction of accelerated MRI acquisitions is proposed using a generative prior based on denoising diffusion models. The novelty of the proposed approach is in modifying the denoising schedule to account for the intrinsic noise in the raw data that is re-introduced during the data consistency stages of the iterative reconstruction. The approach is evaluated in several datasets, and compared to 3 other diffusion-model based reconstruction methods, consistently showing the best results.

  • Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.

    One strength of the paper is it’s strong performance compared to other (uncorrected) reconstruction methods using diffusion priors. Another strength is the novelty of the idea behind incorporating a correction that accounts for the intrinsic noise in the raw measurement data. Finally, the last strength is the simplicity of the correction, making it easy to adopt.

  • Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.

    One weakness is that the proposed linear attenuation function is not fully explained, in that it is not explained how parameters such as gamma are selected, or why the decay function is linear. Furthermore, the impact of reducing the data consistency gradient term as t->0 is not fully explored - does this impact the bias of the proposed method? What are the potential down-sides to the proposed approach?

  • Please rate the clarity and organization of this paper

    Very Good

  • Please comment on the reproducibility of the paper. Please be aware that providing code and data is a plus, but not a requirement for acceptance.

    The submission does not mention open access to source code or data but provides a clear and detailed description of the algorithm to ensure reproducibility.

  • Do you have any additional comments regarding the paper’s reproducibility?

    A clear high level description of the method is provided, although no link to a code repository or mention of the actual ML framework used is provided (as far as I can tell)

  • Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review. Pay specific attention to the different assessment criteria for the different paper categories (MIC, CAI, Clinical Translation of Methodology, Health Equity): https://conferences.miccai.org/2024/en/REVIEWER-GUIDELINES.html

    The paper could benefit from some more detail on the proposed attenuation function, and the specific impact of reducing the data consistency gradient as the iterations increase. As in, it re-normalizes the noise expected by the difusion model, but at the cost of reducing the data consistency. The tradeoff between these constraints could be further explored. In some comparisons, such as the AdaDiff method, the performance seems particularly poor, which begs the question of whether the method was implemented correctly or not.

  • Rate the paper on a scale of 1-6, 6 being the strongest (6-4: accept; 3-1: reject). Please use the entire range of the distribution. Spreading the score helps create a distribution for decision-making

    Accept — should be accepted, independent of rebuttal (5)

  • Please justify your recommendation. What were the major factors that led you to your overall score for this paper?

    The paper shows excellent results, and presents a novel idea (of re-weighting the DC gradient to account for measurement noise). However, minor weaknesses relating to detail on the attenuation function, and any tradeoffs resulting from reducing the DC gradient step weight remain.

  • Reviewer confidence

    Very confident (4)

  • [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed

    N/A

  • [Post rebuttal] Please justify your decision

    N/A



Author Feedback

General Response: The proposed method aims to apply an MRI diffusion model trained on one dataset for reconstructing images from a different dataset with different noise levels. Such discrepancies can disrupt the pre-trained reverse process at time steps corresponding to noise levels lower than those in the k-space data. To address this, we introduce a simple yet effective attenuation function. We have very extensively evaluated this method.

Concern #1 (Eq. 7 Correctness and Approximation Errors) by Reviewer #1. Response: We thank Reviewer #1 for providing relevant references [1,2], but we disagree with the assertion that Eq. 7 is “technically incorrect”.

In short, the basic assumption Eq. 1 of our paper is MRI-specific, making the gradient of p(y x_t) computable and our Eq. 7 technically correct. Our Eq. 1 assumes that the likelihood p(y x) is given by a complex normal distribution for all noise levels, allowing Eq. 7 to be derived directly without approximation errors. In ref [1], the approximation error from their Eq. 15 does not apply to our MRI reconstruction scenarios. Specifically, the noise level of k-space y does not match that of training images, x_0. Therefore, we have directly defined the likelihood function p(y x_t) in our Eq. 1 for all noise levels, without introducing x_0. The gradient of p(y x_t) is thus computable. For details, we refer to the assumption in Eq. 7 in [1], which described the probabilistic flow in Fig.2 in [1].

The KEY question is whether our Eq. 1 is valid in the context of MRI reconstruction? We firmly believe it is. Firstly, this assumption is widely used in MRI research [3,4]. Secondly, our extensive experiments demonstrate that this assumption leads to robust reconstructions. Thirdly, we have internally tested Song’s approach [2], which did not yield advantages.

Nevertheless, we are willing to cite the references [1,2] and clarify that Eq. 1 is an MRI-specific assumption. Additionally, we have missed a scaling coefficient in Eq. 7 when writing the manuscript. The corrected Eq. 7 should be: ∇xt log p(y xt) = -(AHAxt - AHy) / 𝜎_𝜂^2. The coefficient 𝜎_𝜂^2 is later absorbed into the step size during iterations. Note that this intended minor correction is to align with other MRI reconstruction literatures[3,4], not related to approximation errors.

Concern #2 (Attenuation Function Design and Hyperparameters) by all reviewers. Response: The current design of the attenuation function is simple and effective for our purposes. Some justifications can be found in Fig. 2 of the supplementary material, where noise propagating from the MRI data does not significantly impact the total noise level in the early stages Therefore, we did not scale the data consistency term from the beginning. We acknowledge that the attenuation function can be further optimized, and exploring different shapes for the attenuation function is beyond the scope of this study.

We apologize for any confusion regarding the hyperparameters. Our method includes only two hyperparameters: 1) sigma_y and 2) gamma. Parameters k and b can be determined by \sigma_y and \gamma. For \gamma, we fixed its value at 0.2. We will clarify these issues

Responses to other minor concerns: The sigma values in Table 2 represent the added noise. We added noise to fully sampled data and then downsampled it to obtain the measurement y as mentioned in Fig.5 caption. For sigma_y, calibration scans are not always available, but it can be estimated in other practical ways, as mentioned in the paper. We will cite all suggested studies.

References: [1]Chung et al. Diffusion Posterior Sampling for General Noisy Inverse Problems. ICLR, 2022 [2]Song et al. Solving Inverse Problems in Medical Imaging with Score-Based Generative Models. ICLR, 2021 [3]Jalal et al. Robust Compressed Sensing MRI with Deep Generative Priors. NeurIPS 2021 [4]Luo et al. Bayesian MRI Reconstruction with Joint Uncertainty Estimation Using Diffusion Models. MRM, 2023



Meta-Review

Meta-review #1

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’

    Reviewers raised their scores after the rebuttal. I agree with the reviewers judgment and recommend acceptance.

  • What is the rank of this paper among all your rebuttal papers? Use a number between 1/n (best paper in your stack) and n/n (worst paper in your stack of n papers). If this paper is among the bottom 30% of your stack, feel free to use NR (not ranked).

    Reviewers raised their scores after the rebuttal. I agree with the reviewers judgment and recommend acceptance.



Meta-review #2

  • After you have reviewed the rebuttal and updated reviews, please provide your recommendation based on all reviews and the authors’ rebuttal.

    Accept

  • Please justify your recommendation. You may optionally write justifications for ‘accepts’, but are expected to write a justification for ‘rejects’

    Reviewers #1 and #3 increased their scores because of the authors’ clarification and justification in the rebuttal. I agree with the reviewers and recommend acceptance.

  • What is the rank of this paper among all your rebuttal papers? Use a number between 1/n (best paper in your stack) and n/n (worst paper in your stack of n papers). If this paper is among the bottom 30% of your stack, feel free to use NR (not ranked).

    Reviewers #1 and #3 increased their scores because of the authors’ clarification and justification in the rebuttal. I agree with the reviewers and recommend acceptance.



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